On some restrictions of an operator to an invariant subspace - Wójcik, Paweł (Linear algebra and its applications, 2014)
For Banach spaces we consider the bounded linear operators which are surjective and noninjective. We show some general properties of such mappings. We examine whether such operators can be restricted to an involution or a projection. Thus, we will show that there exist many invariant subspaces for those operators. In respect to this, we will understand better the structure of many operators.